Let \(f\) be the function given by \(f(x)=2e^{3x}\) and \(g\) be the function given by \(g(x)=4x^3\). At what value of \(x\) do the graphs of \(f\) and \(g\) have parallel tangent lines?

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Take the derivative of both functions:

Setting the derivative of each function equal to each other:

$$ 6e^{3x}=12x^2 $$

In our calculator, we plot the graph of both derivatives. Use the intersect option to find the \(x\) value that corresponds to the solution.

$$ x \approx \boxed{-0.39} $$